Let T be the tetrahedron with vertices at the origin and (5,0,0), (0,5,0) and (0,0,6). A fluid flows with velocity (xe", y, – ze"), where position is measured in meters, and speed is measured in meters per second. Find the rate of flow outward through the slant surface of the tetrahedron, which is the only face that is not parallel to any of the coordinate planes. -
Let T be the tetrahedron with vertices at the origin and (5,0,0), (0,5,0) and (0,0,6). A fluid flows with velocity (xe", y, – ze"), where position is measured in meters, and speed is measured in meters per second. Find the rate of flow outward through the slant surface of the tetrahedron, which is the only face that is not parallel to any of the coordinate planes. -
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Transcribed Image Text:Let T be the tetrahedron with vertices at the origin and
(5,0,0), (0,5,0) and (0,0,6). A fluid flows with velocity
(xe", y, – ze"), where position is measured in meters,
-
and speed is measured in meters per second. Find the rate
of flow outward through the slant surface of the
tetrahedron, which is the only face that is not parallel to
any of the coordinate planes.
Hint: Using the Divergence Theorem, the problem can be
done with geometry only and not evaluating any integrals.
m3
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